In a single-slit diffraction experiment, the position of the diffraction minima is given by the condition:
asin‌θ=nλwhere
a is the slit width,
θ is the angle of diffraction,
n is the order of the minimum, and
λ is the wavelength of light.
Let's denote the two wavelengths by
λ1 and
λ2. According to the problem, the
2‌nd ‌ order diffraction minimum for
λ1 coincides with the
3‌rd ‌ order diffraction minimum for
λ2. This can be written as:
asin‌θ=2λ1and
asin‌θ=3λ2Since both conditions are satisfied simultaneously at the same angle
θ, we can equate the two expressions:
square2λ1=3λ2Thus, the ratio of the wavelengths is:
‌=‌Therefore, the correct option is:
Option C:
‌=‌